Toward the terminate of seventh grade, my middle-school band took a trip to Cedar Point, which was pretty much the theme park to which midwestern middle-school bands traveled. (I imagine it still is.)  They had this indoor roller coaster there, called the Disaster Transport. My friends and I were standing in line for this roller coaster, winding up the dimly lit cement steps, when nosotros turned a corner and came across a huge pile of money.

Nosotros picked it up and counted it; it was a very specific amount of money. I don't recollect now exactly how much, but for the purposes of this retelling, permit'due south say information technology was $134. That sounds shut.

We had barely had fourth dimension to whiplash from marveling at our good fortune to guiltily suggesting we should find somewhere to plow information technology in before a group of older kids ahead of u.s.a. snatched the cash wad out of our hands. They claimed it was theirs; it was non theirs—they counted it in front of us and exchanged "Whoa"s and high fives. We were hapless, gangly middle schoolers (I was growing out my bangs; information technology was a crude year). They were confident nosotros would do zero to stop them, and they were right. And so that was the end of that.

Until, Part 2:

A petty more than a year afterward, I went to a summer programme at Michigan Country University, a nerd campsite where you take classes similar genetics for fun. One evening, as we were sitting around in the common area, chatting and doing homework, I overheard a kid telling his friends how he'd lost a agglomeration of money concluding twelvemonth at Cedar Bespeak.

With very trivial endeavour at arctic I interrupted their chat and grilled him on the particulars.

Was he there on May whatever date I was also there? He was.

Did he lose the money in line for the Disaster Transport? In fact, he did.

How much money did he lose? $134, exactly.

* * *

Though "What are the odds?" is pretty much the catchphrase of coincidences, a coincidence is non just something that was unlikely to happen. The overstuffed crate labeled "coincidences" is packed with an astonishing multifariousness of experiences, and nonetheless something more than than rarity compels us to grouping them together. They have a similar texture, a feeling that the cloth of life has rippled. The question is where this feeling comes from, why we discover certain means the threads of our lives collide, and ignore others.

Some might say it's but because people don't sympathise probability. In their 1989 paper "Methods for Studying Coincidences," the mathematicians Persi Diaconis and Frederick Mosteller considered defining a coincidence as "a rare consequence," but decided "this includes too much to let conscientious study." Instead, they settled on, "A coincidence is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection."

From a purely statistical point of view, these events are random, not meaningfully related, and they shouldn't exist that surprising because they happen all the fourth dimension. "Extremely improbable events are commonplace," as the statistician David Hand says in his book The Improbability Principle. Just humans generally aren't great at reasoning objectively near probability as they get about their everyday lives.

For one thing, people tin can exist pretty liberal with what they consider coincidences. If you lot come across someone who shares your birthday, that seems like a fun coincidence, but you might feel the same manner if you met someone who shared your female parent'due south birthday, or your best friend's. Or if it was the twenty-four hour period correct before or afterward yours. So there are several birthdays that person could have that would feel coincidental.

And there are lots of people on this planet—more than than seven billion, in fact. According to the Police of Truly Large Numbers, "with a large enough sample, any outrageous thing is likely to happen," Diaconis and Mosteller write. If enough people buy tickets, there will exist a Powerball winner. To the person who wins, it's surprising and miraculous, but the fact that someone won doesn't surprise the rest of u.s..

Even inside the relatively limited sample of your ain life, at that place are all kinds of opportunities for coincidences to happen. When you consider all the people you lot know and all the places you lot go and all the places they go, chances are proficient that you'll see someone you know, somewhere, at some signal. But it'll however seem like a coincidence when you do. When something surprising happens, nosotros don't think virtually all the times it could have happened, but didn't. And when nosotros include most misses every bit coincidences (you and your friend were in the aforementioned place on the same twenty-four hour period, just not at the same time), the number of possible coincidences is suddenly way greater.

To demonstrate how common unlikely seeming events can exist, mathematicians similar to trot out what is called the birthday problem. The question is how many people need to be in a room earlier there's a 50/l gamble that two of them will share the same birthday. The answer is 23.

"Oh, those guys and their birthdays really become me mad," says Bernard Beitman, a psychiatrist and visiting professor at the University of Virginia, and author of the forthcoming book Connecting With Coincidence . That'southward not the manner the average person would frame that question, he says. When someone asks "What are the odds?" odds are they aren't asking, "What are the odds that a coincidence of this nature would have happened to anyone in the room?" but something more like, "What are the odds that this specific thing would happen to me, here and now?" And with anything more complicated than a birthday match, that becomes almost impossible to calculate.

Information technology's true that people are fairly egocentric about their coincidences. The psychologist Ruma Falk institute in a study that people rate their own coincidences equally more surprising than other people's. They're similar dreams—mine are more interesting than yours.

"A coincidence itself is in the eye of the beholder," says David Spiegelhalter, the Winton Professor for the Public Understanding of Take chances at the University of Cambridge. If a rare result happens in a forest and no one notices and no one cares, it's non really a coincidence.

* * *

I told Spiegelhalter my Cedar Point story on the telephone—I couldn't help information technology. He collects coincidences, run into. (A thriller novel called The Coincidence Authority has a professor character based on him.) He has a website where people can submit them, and says he's gotten about 4,000 or 5,000 stories since 2011. Unfortunately, he and his colleagues haven't washed much with this treasure trove of information, more often than not because a pile of complimentary-form stories is a pretty difficult data prepare to measure. They're looking for someone to practise text-mining on it, but then far all they've been able to clarify is how many coincidences fall into the different categories y'all tin check off when yous submit your story:

Common Types of Coincidences

David Spiegelhalter

He says he'd categorize mine every bit "finding a link with someone you come across." "But information technology'south a very different sort of connexion," he says, "not like having lived in the same house or something like that. And it's a very stiff one, it's not just similar you were both at the theme park. I love that. And you lot remember information technology after all this time."

And the craziest matter is non that I found someone's money and then that I was in a room with him a year later, but that I institute out about it at all. What if he hadn't brought it up? Or "y'all might non have heard him if you lot'd been somewhere slightly away," Spiegelhalter says. "And yet the coincidence would have been in that location. You would accept been vi feet away from someone who lost their money. The coincidence in a sense would accept physically occurred. It was only because yous were listening that you noticed it. And then that's why the amazing thing is not that these things occur, it's that nosotros notice them."

"This is my large theory about coincidences," he continues, "that's why they happen to certain kinds of people."

Beitman in his enquiry has establish that certain personality traits are linked to experiencing more than coincidences—people who describe themselves as religious or spiritual, people who are self-referential (or likely to chronicle information from the external world back to themselves), and people who are high in meaning-seeking are all coincidence-prone. People are likewise likely to see coincidences when they are extremely deplorable, angry, or anxious.

"Coincidences never happen to me at all, because I never notice annihilation," Spiegelhalter says. "I never talk to anybody on trains. If I'm with a stranger, I don't try to notice a connexion with them, because I'm English."

Beitman, on the other hand, says, "My life is littered with coincidences." He tells me a story of how he lost his domestic dog when he was eight or 9 years old. He went to the law station to ask if they had seen it; they hadn't. Then, "I was crying a lot and took the wrong way home, and there was the dog … I got into [studying coincidences] just because, hey, await Bernie, what's going on hither?"

For Beitman, probability is not enough when it comes to studying coincidences. Because statistics can depict what happens, simply tin't explain information technology any further than chance. "I know there'due south something more going on than we pay attention to," he says. "Random is not enough of an explanation for me."

Random wasn't enough for the Swiss psychiatrist Carl Jung either. And then he came upward with an alternative explanation. Coincidences were, to him, meaningful events that couldn't be explained by cause and effect, which, so far so good, only he also thought that there was some other force, outside of causality, which could explain them. This he called "synchronicity," which in his 1952 volume, he called an "acausal connecting principle."

Meaningful coincidences were produced by the strength of synchronicity, and could be considered glimpses into another of Jung'south ideas—the unus mundus, or "i world." Unus mundus is the theory that there is an underlying order and structure to reality, a network that connects everything and everyone.

For Jung, synchronicity didn't just business relationship for coincidences, but also ESP, telepathy, and ghosts. And to this 24-hour interval, inquiry shows that people who feel more coincidences tend to be more probable to believe in the occult besides.

This is the problem with trying to observe a deeper caption for coincidences than randomness—information technology tin can rapidly veer into the paranormal.

* * *

Beitman, like Spiegelhalter, is interested in sorting and labeling dissimilar kinds of coincidences, to develop categories "like an early botanist," he says, though his categories are more expansive and include not but things that happen in the world just people'due south thoughts and feelings equally well. In our conversation, he divides coincidences into three wide categories—environment-surround interactions, mind-environment interactions, and mind-mind interactions.

Environment-environment are the most obvious, and easiest to empathise. These coincidences are objectively appreciable. Something, or a series of things, happens in the physical world. Y'all're at a gin articulation in Morocco and your long-lost dearest from Paris shows upwardly. I institute some money and a year afterwards I met the person who lost it.

A nurse named Violet Jessop was a stewardess for White Star Line and lived through three crashes of its ill-blighted armada of bounding main liners. She was on the Olympic when it collided with the HMS Hawke in 1911. In 1912, she was in that location for the big one: the Titanic. And iv years later on, when White Star'south Britannic, reportedly improved after its sister ship'southward disaster, too sank, Jessop was there. And she survived. That ane, I guess, is an surround-surround-environment.

Mind-environment coincidences are premonition-esque—you're thinking of a friend and then they call you, for example. Simply unless you lot happen to write down "I am thinking of so-and-and then [timestamp]" before the call happens, these are absurd for the person they happen to, but not really measurable. "We banned premonitions from our site," Spiegelhalter says. "Because, where's the proof? Everyone could say anything."

Some other sort of mind-environment interaction is learning a new word so of a sudden seeing it everywhere. Or getting a vocal stuck in your head and hearing it everywhere you become, or wondering well-nigh something and and then stumbling onto an article about it. The things on our minds seem to bleed out into the globe around us. But, though information technology makes them no less magical, life'southward motifs are created not past the world around us, but past humans, by our attention.

This is an effect that the Stanford linguistics professor Arnold Zwicky calls "the frequency illusion," and it's not the same every bit a premonition. Information technology'due south just that once you've noticed something, your brain is primed to notice information technology again the side by side fourth dimension you lot see it. A give-and-take or a concept you've just learned feels relevant to you—you may accept seen it hundreds of times earlier and just never noticed. But now that you lot're paying attention, it's more likely to pop out at you lot the next time it whizzes by.

And so the final category, listen-mind, of course, is straight-up mystical. One case of this is "simulpathity," a term Beitman coined to describe feeling the pain or emotion of someone else at a distance. His interest in this item type of coincidence is deeply personal.

"In San Francisco, in 1973, February 26, I stood at a sink uncontrollably choking," he says, clarifying, "In that location was nothing in my throat that I knew [of]."

"It was around 11 o'clock in San Francisco. The next solar day my blood brother chosen, and told me my father had died at 2 a.yard. in Wilmington, Delaware, which was xi in San Francisco, and he had died by choking on blood in his throat. That was a dramatic experience for me, and I began to await to see if other people had experiences similar this. And many people have."

* * *

This is where nosotros start to leave the realm of science and enter the realm of belief. Coincidences are remarkable in how they straddle these worlds. People take surprising, connective experiences, and they either create pregnant out of them, or they don't.

Leaving a coincidence as goose egg more than a curiosity may exist a more than prove-based mindset, merely it's not fair to say that the people who brand significant from coincidences are irrational. The process by which we notice coincidences is "part of a general cognitive architecture which is designed to make sense of the earth," says Magda Osman, an associate professor in experimental psychology at Queen Mary University of London. It'south the same rational process we use to learn crusade and effect. This is one way to scientifically explicate how coincidences happen—as past-products of the brain's pregnant-making system.

People like patterns. Nosotros look for them everywhere, and by noticing and analyzing them nosotros can understand our world and, to some small degree, control it. If every fourth dimension you motion picture a switch, a lamp across the room turns on, yous come to understand that that switch controls that lamp.

When someone sees a pattern in a coincidence, "in that location's no fashion I tin say 'Yeah, that was definitely a run a risk result,' or 'There was an actual causal mechanism for it,' considering I'd take to know the world perfectly to be able to say that," Osman says.

Instead what we do is weigh whether information technology seems likelier that the event was acquired by chance, or by something else. If take a chance is the winner, we dismiss it. If not, we've got a new hypothesis about how the world works.

Take the instance of ii twins, who were adopted past dissimilar families when they were four weeks one-time. When they were afterward reunited, their lives had … a lot of similarities. They were both named James by their adoptive families, were both married to a Betty and had divorced a Linda. One twin's outset son'southward proper name was James Alan, the other's was James Allan. They both had adoptive brothers named Larry and pet dogs named Toy. They both suffered from tension headaches, and both vacationed in Florida within three blocks of each other.

You could hypothesize from this that the ability of genetics is so stiff, that even when identical twins are separated, their lives play out the same fashion. In fact, the twins were office of a University of Minnesota written report on twins reared autonomously that was asking just that question, though information technology didn't suggest that there was any cistron that would brand someone attracted to a Betty, or probable to name a dog Toy.

Cartoon inferences from patterns like this is an advantageous matter to exercise, even when the pattern isn't 100 per centum consequent. Take learning language as an example. In that location isn't going to be a domestic dog, or even a film of a dog, nearby every time a kid hears the word "domestic dog." But if dad points at the family unit Fido enough times while saying "dog," the kid volition learn what the word means anyhow.

"Small-scale children are justified in being conspiracy theorists, since their globe is run by an inscrutable and all-powerful organisation possessing secret communications and mysterious powers—a world of adults, who act past a system of rules that children gradually primary as they abound upwardly," write the cognitive scientists Thomas Griffiths and Joshua Tenenbaum in a 2006 study on coincidences.

Nosotros retain this adequacy, even when nosotros're older and accept figured out most of these more obvious patterns. It can however be very useful, specially for scientists who are working on unsolved questions, but for most adults in their daily lives, any new casual connection is likely to be specious. From a scientific perspective, anyway. If we realize that, so we wave it off as "just a coincidence," or what Griffiths, a professor of psychology and cognitive scientific discipline at the Academy of California, Berkeley, calls a "mere coincidence."

On the flip side, for someone who believes in ESP, thinking of a friend correct before she calls may not exist a coincidence to them at all, only just more evidence to back up what they already believe. The same goes for someone who believes in divine intervention—a chance meeting with a long-lost lover may be, to them, a sign from God, non a coincidence at all.

"You really come across a question of only what belief organisation you have almost how reality works," Beitman says. "Are you a person who believes the universe is random or are you a person who believes there's something going on here that maybe we gotta pay more attention to? On the continuum of explanation, on the left-hand side nosotros've got random, on the right-hand side we've got God. In the heart nosotros've got little Bernie Beitman did something here, I did information technology simply I didn't know how I did it."

In the middle zone prevarication what Griffiths calls "suspicious coincidences."

"To me, that'southward a primal office of what makes something a coincidence—that it falls in that realm betwixt being certain that something is false and being certain that something is true," he says. If enough suspicious coincidences of a certain nature pile up, someone's dubiety can cross over into belief. People can stumble into scientific discoveries this style—"Hmm, all these people with cholera seem to be getting their h2o from the same well"—or into superstition—"Every time I vesture mismatched socks, my meetings get well."

But you tin can stay in that in-between zone for a long time—suspicious, only unsure. And this is nowhere more obvious than in the coincidences that present every bit prove for some kind of subconscious simply as-even so undiscovered ordering principle for reality, exist that synchronicity or a sort of David Mitchell–esque "Everything Is Connected" spider web that ensnares us in its design. Meaningful connections can seem created by design—things are "meant to be," they're happening for a reason, even if the reason is elusive. Or as Beitman puts information technology, "Coincidences warning the states to the mysterious hiding in plain sight."

I suppose no one can prove in that location isn't such a matter, just information technology's definitely incommunicable to prove that there is. And then you're left with … not much. Where you fall on the continuum of explanation probably says more most you than it does about reality.

* * *

In The Improbability Principle, Mitt cites a 1988 U.S. National Academy of Sciences report that concluded that at that place was "no scientific justification from research conducted over a period of 130 years for the beingness of parapsychological phenomena."

"I hundred thirty years!" Manus writes. The fact that people kept trying to find proof for the paranormal was "a testament to the power of hope over experience if there ever was one."

But I disagree. It may be that researching the paranormal is partly an act of hope that you'll observe something where no 1 has found anything before. But it seems like, often, experiences are the building blocks of belief in the paranormal, or in an underlying force that organizes reality. Even if they're not doing formal research, people are seeking explanations for their experiences. And construction is a much more than highly-seasoned caption than adventure.

Where you fall on the chance-structure continuum may have a lot to do with what you think run a risk looks like in the showtime identify. Enquiry shows that while most people are pretty bad at generating a random string of numbers, people who believe in ESP are even worse. Even more so than skeptics, believers tend to think that repetitions in a sequence are less probable to be random—that a coin flip sequence that went "heads, heads, heads, heads, tails" would be less probable to come randomly than 1 that went "heads, tails, heads, tails, heads," fifty-fifty though they're equally likely.

So we have psychology to explain how and why nosotros notice coincidences, and why we want to make significant from them, and we have probability to explicate why they seem to happen so often. But to explicate why whatsoever private coincidence happened involves a snarl of threads, of decisions and circumstances and bondage of events that, even if i could untangle it, wouldn't tell you lot anything about any other coincidence.

Jung seems to have been annoyed past this. "To grasp these unique or rare events at all, nosotros seem to be dependent on equally 'unique' and individual descriptions," he writes, despairing of the lack of a unifying theory offered by scientific discipline for these strange happenings. "This would outcome in a chaotic collection of curiosities, rather like those old natural-history cabinets where one finds, cheek past jowl with fossils and anatomical monsters in bottles, the horn of a unicorn, a mandragora manikin, and a stale mermaid."

This is supposed to be unappealing (surely these things should exist put in order!), simply I rather like the paradigm of coincidences equally a curio chiffonier full of odds and ends we couldn't detect anywhere else to put. Information technology may not exist what we're almost comfortable with, but a "cluttered collection of curiosities" is what we've got.